Inverse nodal problems of discontinuous Sturm-Liouville operator

We study inverse nodal problems for the second-order differential operator with discontinuity inside a finite interval. In particular, we solve the uniqueness, reconstruction and stability problems using the nodal set of its eigenfunctions. Furthermore, we show that the space of discontinuous Sturm-Liouville operators characterized by B = (q, h, H, a(1), a(2)) is an element of L-1 (0,1) X R-4 such that integral(1)(0) q(x)dx = 0 is homeomorphic to the partition set of the space of quasinodal sequences, which are all admissible sequences X = {X-n(j)}(n >= 2,j=/1,n-1) which form sequences that converge to q, h, H, and 2a(2)/a(1)+a(1)(-1) individually. (C) 2012 Elsevier Inc. All rights reserved.